1 Errors & Significance
A STAT 200 instructor wants to compare the final exam scores of students taught using two different curricula. She obtains a sample of 500 students. She randomly assigns 250 students to a traditional curriculum and 250 students to a new curriculum. It is hypothesized that the new curriculum will lead to higher scores. If there is no significant difference between the exam scores of the different teaching methods, she will continue to teach using the older curriculum. If there is a significant difference, then she will publish a new course using the new curriculum.
a. State the null and alternative hypotheses that the instructor should test. Use μ1 to denote the mean final exam score of students in the traditional curriculum group and μ2 to denote the mean final exam score of students in the new curriculum group.
b. Type I error:
i. What does a Type I error mean in this situation?
ii. What are the consequences of making a Type I error in this scenario?
c. Type II error:
i. What does a Type II error mean in this situation?
ii. What are the consequences of making a Type II error in this scenario?
d. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning.
e. If you were working with this researcher, what alpha level would you use and why?
Assume that the instructor completes this study and finds μ1 = 41 and μ2 = 40 with a pooled standard deviation of 7. Her p-value is 0.0413.
f. Compute Cohen's d as a measure of effect size.
g. Using the alpha level you selected in part e, are her results statistically significant? Explain why or why not.
h. Are her results practically significant? Explain why or why not.
2 Confidence Intervals & Hypothesis Tests
The manager of a restaurant wants to know if there is a correlation between the amount of a customer's bill and the percent that they tip. In other words, as people spend more money, do they tend to tip at different rates? With data from a random sample of 157 receipts, he used StatKey to construct a 95% bootstrap confidence interval for ρ. The results were: [0.018, 0.292].
a. If the manager wanted to conduct a hypothesis test instead, what would be the appropriate null and alternative hypotheses?
b. Based on the 95% confidence interval, would you expect the manager to reject or fail to reject the null hypothesis at the 0.05 alpha level? Explain your reasoning.
c. Using this scenario, compare and contrast confidence intervals and hypothesis testing. List at least one similarity and at least one difference.
3 Hypothesis Tests
A researcher wants to compare the means of 4 different groups. What procedure(s) should he use and why?
Answered in over 550 words. Explanations have been given for answers. Calculations and statistical notations are shown using Word equation editor. Computed answers have been rounded to 3 decimal places.